\newproblem{lay:2_9_23}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.9.23}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Nov. 11th, 2013} \\}{}

  % Problem statement
	If possible, construct a $3\times 5$ matrix such that $\dim\{\mathrm{Nul}\{A\}\}=3$ and $\dim\{\mathrm{Col}\{A\}\}=2$.
}{
  % Solution
	Consider the matrix $A=\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 \end{pmatrix}$. The dimension of its column space is given by the number of
	pivot columns (columns 1 and 4 are pivot columns), while the dimension of its null space is given by the number of non-pivot columns (columns 2, 3 and 5 are non-pivot).
}
\useproblem{lay:2_9_23}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
